Do Apparel Stores Have a Higher Return on Equity (ROE) than Department Stores?

 

 

My population is the return on equity in all years for all apparel stores and return on equity in all years for all department stores.  The parameters are the mean return on equity for all apparel stores and the mean return on equity for all department stores.  The samples are 51 apparel stores and 30 department stores from Yahoo Finance on November 6, 2013.  I eliminated stores for which Yahoo did not have a ROE or that had negative ROE.  The statistics are the mean return on equity for 51 apparel stores which was 19.30and the mean return on equity for 30 department stores which was 16.47%.

 

Presentation of the data:

 

	Department Store	ROE %						cumulative
	lower		upper	midpoint	width	frequency	percent	frequency	percent
	0.00	<	5.00	2.50	5.00	5	16.7	5	16.7
	5.00	<	10.00	7.50	5.00	4	13.3	9	30.0
	10.00	<	15.00	12.50	5.00	7	23.3	16	53.3
	15.00	<	20.00	17.50	5.00	7	23.3	23	76.7
	20.00	<	25.00	22.50	5.00	3	10.0	26	86.7
	25.00	<	30.00	27.50	5.00	1	3.3	27	90.0
	30.00	<	35.00	32.50	5.00	0	0.0	27	90.0
	35.00	<	40.00	37.50	5.00	0	0.0	27	90.0
	40.00	<	45.00	42.50	5.00	1	3.3	28	93.3
	45.00	<	50.00	47.50	5.00	1	3.3	29	96.7
	50.00	<	55.00	52.50	5.00	0	0.0	29	96.7
	55.00	<	60.00	57.50	5.00	1	3.3	30	100.0
						30	100.0

 

 

Department Store
	ROE %
count	30
mean	16.41727
sample standard deviation	12.64181
sample variance	159.81544
minimum	0.599
maximum	55.215
range	54.616

 

	Apparel stores	ROE %						cumulative
	lower		upper	midpoint	width	frequency	percent	frequency	percent
	0.00	<	10.00	5.00	10.00	12	23.5	12	23.5
	10.00	<	20.00	15.00	10.00	22	43.1	34	66.7
	20.00	<	30.00	25.00	10.00	8	15.7	42	82.4
	30.00	<	40.00	35.00	10.00	3	5.9	45	88.2
	40.00	<	50.00	45.00	10.00	4	7.8	49	96.1
	50.00	<	60.00	55.00	10.00	1	2.0	50	98.0
	60.00	<	70.00	65.00	10.00	0	0.0	50	98.0
	70.00	<	80.00	75.00	10.00	1	2.0	51	100.0
						51	100.0

 

 

Apparel stores
	ROE %
count	51
mean	19.29759
sample standard deviation	14.90353
sample variance	222.11522
minimum	1.057
maximum	71.474
range	70.417

 

 

Hypothesis test:

Ho:  µ_Ap  ≥ µ_{Dept   or}  µ_Ap – µ_Dept  ≥  0

HA:  µ_Ap  < µ_{Dept or} µ_Ap – µ_Dept  <  0

T_crit   = 2.462 ( using α = 0.01 in one tail and df = n – 1 = 30 – 1 =29 using the smaller of the sample sizes) In Excel, t.inv(.99,29)

Fail to reject Ho.  The 2.88% difference between the mean return on equity for apparel companies and the mean return on equity of department stores is not sufficient evidence to prove that the apparel companies have a significantly higher return on equity than department stores, on average.  There was quite a bit of variation within the two data sets which resulted in me not being confident in the difference I found between the two means.  Note that both had distributions that are skewed to the right, but since the sample sizes both exceed 30, I was able to use the normal distribution in the analysis.

 

 

Appendix:  Data table:

Department Stores			Apparel Stores
	ROE %			ROE %
Kirkcaldie & Stains Limited	0.599		Ocean Sky International Ltd.	1.057
Bon-Ton Stores Inc.	0.616		Destination XL Group, Inc.	1.273
Grupo Elektra, S.A. de C.V.	1.769		Reitmans (Canada) Limited	1.437
Saks Incorporated	3.768		Reitmans (Canada) Limited	1.437
Metro Holdings Limited	4.656		LeRoi Holdings Ltd.	2.658
Sears Hometown and Outlet Stor	7.496		Etam Developpement SA	4.509
Grupo Famsa SAB de CV	7.931		New York & Company Inc.	5.409
Lianhua Supermarket	8.176		Stage Stores Inc.	6.578
Organizacion Soriana	8.846		Moss Bros Group PLC	6.944
New World Depa.Store Chin	10.184		The Children	8.954
Sears Canada Inc.	11.801		Joyce Boutique Holdings Ltd.	9.081
Parkson Retail Group Ltd.	11.987		Jos. A Bank Clothiers Inc.	9.744
David Jones Limited	12.073		Shoe Carnival Inc.	10.13
Wing On Company Inter	14.091		Evergreen International	10.507
Century Ginwa Retail	14.306		Ascena Retail Group Inc.	10.713
Intime Department Store Group	14.585		Stein Mart Inc.	11.616
Springland International	15.368		The Men’s Wearhouse, Inc.	11.701
Kohl’s Corp.	15.848		I.T Ltd.	12.178
Services	16.887		Trinity Ltd.	12.875
Marks & Spencer Group PLC	17.397		Genesco Inc.	13.012
Dillard’s Inc.	18.037		Premier Investments Limited	13.683
Debenhams PLC	18.201		Abercrombie & Fitch Co.	14.525
Patagonia	19.034		The Cato Corporation	14.8
Macy’s, Inc.	23.354		Luxottica Group S.p.A.	14.812
Lifestyle International	23.667		Luxottica Group SpA	14.812
Ashley (Laura) Holdings PLC	24.18		Goldlion Holdings Ltd.	15.036
Golden Eagle Retail Group Ltd.	25.666		Guess’ Inc.	15.107
Warehouse Group Limited (The)	41.039		Kathmandu Holdings Limited	15.396
China Seven Star Shopping Ltd.	45.741		Chico’s FAS Inc.	15.435
The TJX Companies, Inc.	55.215		DSW Inc.	15.884
			Xtep International	15.929
			American Eagle Outfitters, Inc	16.762
			OrotonGroup Limited	17.265
			Urban Outfitters Inc.	19.715
			Specialty Fashion	21.308
			Destination Maternity Corporat	21.362
			Marisa Lojas SA	22.836
			Casual Male Retail Group, Inc.	25.52
			ANN INC.	25.902
			Tilly’s, Inc.	25.966
			Hallenstein Glasson Limited	27.969
			Giordano International Ltd.	29.615
			Industria De Diseno Textil SA	30.974
			Express Inc.	36.534
			Nordstrom Inc.	39.255
			The Gap, Inc.	40.749
			The Buckle, Inc.	44.135
			Ross Stores Inc.	46.945
			Cherokee Inc.	47.444
			TJX Companies	55.215
			Francesca’s Holdings Corporati	71.474